This is not currently possible. The Tableau feature for impersonation relies on specific syntax in SQL Server for managing the state of impersonation.
We may consider future support for other databases which have features for managing impersonation, however there are no immediate plans to do so. If this is an important feature to you, please contact your Sales rep to explain your needs and the ways that this feature might expand your company's use of Tableau. This will help us weigh the priority of the feature with many other great feature requests we receive.
I see this as a fairly old response. Do we have a provision for this now? Is it possible to let us know about the specific syntax that SQL Server uses?